In matrix form this would be
.
Can you go from here?
Huh? Try a = 2, b = 4, c = -6, x = 1, y = 5
That's a solution for both equations.....but x<>c and y<>-a
There are many other similar cases.
Did I miss something?
Also, equations can be re-arranged this way:
ax + bx + cy = bc [1]
-ax - by - cy = ab [2]
===============
bx - by = ab + bc
x - y = a + c